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Math lesson plan · 8th grade (Year 9 in England) · 30 minutes

Write y = mx + b from a slope and intercept, or from a graph

Algebra

CCSS 8.F.B.4CCSS 8.EE.B.6England: KS3 AlgebraEngland: GCSE Foundation Algebra

Objective and success criteria

Students will: Write y = mx + b from a slope and intercept, or from a graph.

  • I can answer questions on today's skill on my own, without help.
  • I can explain each step and say why it works.
  • I can check my answer and spot a mistake.

Before and after

Needs first: Find the y-intercept from an equation, table or graph; Find the slope from a graph using rise over run

Leads to: Find the equation of a line through two points; Rearrange ax + by = c to find slope and intercept; Interpret rate of change and initial value in context

Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).

Warm-up · 4 min

  • Quick retrieval from earlier learning (Find the y-intercept from an equation, table or graph; Find the slope from a graph using rise over run). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. What is the y-intercept of y = 4x − 7? → -7Prompt: The y-intercept is the value of y when x = 0.
  2. x: 1, 2, 3, 4. y: 7, 12, 17, 22. The pattern is linear. What is the y-intercept? → 2Prompt: Work out how much y changes when x goes up by 1.
  3. What is the y-intercept of y = 5x + 10? → 10Prompt: The y-intercept is the value of y when x = 0.

Hook · 3 min

  • Show a "think of a number" puzzle and ask the class to work out the starting number.
  • Share the objective: Write y = mx + b from a slope and intercept, or from a graph. Read the success criteria together.

I do: model it · 7 min

  • Work through the example out loud, saying why you do each step, not just what you do.
  • Example: Write the equation of the line with slope −5 and y-intercept 5. Type the right-hand side (y = …).
  • Step 1: y = −5x + 5
  • Answer: -5x+5
  • Pause after each step and ask a student to say what comes next.

We do: guided practice · 6 min

  • Do these together. Students try each step on whiteboards before you reveal it.
  • Use the hints as prompts rather than giving the answer.
  1. Write the equation of the line with slope −6 and y-intercept 0. Type the right-hand side (y = …). → -6xPrompt: Use y = mx + b.
  2. Omar says the line through (0, 0) with slope 1 is y = x + 1. Write the correct equation. Type the right-hand side. → xPrompt: Omar swapped the slope and the intercept.

You do: independent practice · 7 min

  • Students work on the student sheet. Circulate and check the first two answers of every student early.
  • Students who finish: write a question of their own for a partner, with the answer.

The 6 questions are on the student sheet below, with answers in the key.

Exit ticket · 3 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. Daniel says the line through (0, 4) with slope 2 is y = 4x + 2. Write the correct equation. Type the right-hand side. → 2x+4Prompt: Daniel swapped the slope and the intercept.
  2. Write the equation of the line with slope −5 and y-intercept 3. Type the right-hand side (y = …). → -5x+3Prompt: Use y = mx + b.

Watch out for

  • Doing an operation to one side of an equation but not the other.
  • Reading 3x as 3 + x, or thinking x always stands for one particular number.

Support and stretch

Support

  • Review first: Find the y-intercept from an equation, table or graph.
  • Use concrete materials: balance scales or a balance drawing.
  • Give the first step of each question, or a partly worked example to finish.
  • Pair with a confident partner for the guided practice.

Stretch

  • Move on to: Find the equation of a line through two points; Rearrange ax + by = c to find slope and intercept; Interpret rate of change and initial value in context.
  • Explain a common mistake in writing and how to fix it.
  • Write a word problem that uses today's skill, then solve a partner's.

Homework and more practice

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-8.

Free lesson plan from eurekami.com/lesson-plan-builder

eurekami

Write y = mx + b from a slope and intercept, or from a graph

Name

Date

Score/ 6

  1. Question 1

    Write the equation of the line with slope 1 and y-intercept 6. Type the right-hand side (y = …).

    Answer

  2. Question 2

    Write the equation of the line shown. Type the right-hand side (y = …).

    xy−66−12−66120y = 2x + 1(0, 1)(2, 5)

    Answer

  3. Question 3

    Kofi says the line through (0, −4) with slope 2 is y = −4x + 2. Write the correct equation. Type the right-hand side.

    Answer

  4. Question 4

    Write the equation of the line with slope 6 and y-intercept 7. Type the right-hand side (y = …).

    Answer

  5. Question 5

    Ravi says the line through (0, −1) with slope 3 is y = −x + 3. Write the correct equation. Type the right-hand side.

    Answer

  6. Question 6

    Write the equation of the line with slope −6 and y-intercept −6. Type the right-hand side (y = …).

    Answer

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Answer key: Write y = mx + b from a slope and intercept, or from a graph

  1. 1. x+6

  2. 2. 2x+1

  3. 3. 2x-4

  4. 4. 6x+7

  5. 5. 3x-1

  6. 6. -6x-6